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The gamma function  is the main example of a group of functions collectively referred to as gamma functions. For example, it can be written in terms of the incomplete gamma function:
All four incomplete gamma functions  ,  ,  , and  can be represented as cases of the hypergeometric function  . Further, the gamma function Γ(z) is the special degenerate case of the hypergeometric function  .
The gamma function  and two factorial functions are connected by the formulas:
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